In all, 126 people were freed at the Splendid Hotel in the West African state's capital, Ouagadougou, the interior minister said.
Three gunmen were killed, he added, amid reports of 20 deaths during the attack, which also targeted a cafe.
French Special Forces are helping local troops in the security operation.
French President Francois Hollande has condemned the "odious" attack on the former French colony.
Al-Qaeda in the Islamic Maghreb (AQIM) has said it carried out the attack in the West African nation, monitors said.
In November, an AQIM attack on a hotel in the Malian capital Bamako left 19 people dead.
The SITE monitoring group, which analyses jihadist networks, reports that al-Qaeda in the Islamic Maghreb (AQIM), has said it was behind the attack.
The monitoring group specifically stated that those responsible were the al-Murabitoun group, which is based in the Sahara desert in northern Mali and contains fighters loyal to the veteran Algerian militant Mokhtar Belmokhtar.
Last month, the group announced it had merged with AQIM. Belmokhtar, a one-eyed commander who fought Soviet forces in Afghanistan in the 1980s, was once a member of AQIM but left after a falling-out with its leadership.
Belmokhtar has been declared dead many times, the latest by a US air strike on 14 June last year in Libya - according to Libyan authorities - but his death has not been formally confirmed.
AQIM and al-Murabitoun said they were behind an attack on a hotel in Burkina Faso's neighbour Mali in November that left 20 people dead.